Systems and methods providing electron beam writing to a medium

ABSTRACT

A method for electron-beam writing to a medium includes positioning the medium within an e-beam writing machine so that the medium is supported by a stage and is exposed to an e-beam source. The method also includes writing a pattern to the medium using a plurality of independently-controllable beams of the e-beam source, in which the pattern comprises a plurality of parallel strips. Each of the parallel strips is written using multiple ones of the independently-controllable beams.

CROSS-REFERENCE

This application is a continuation of U.S. Non-provisional PatentApplication Ser. No. 13/757,494, filed on Feb. 1, 2013, entitled“Systems and Methods Providing Electron Beam Writing To A Medium”, nowU.S. Pat. No. 8,610,083, issued Dec. 17, 2013 which is a continuation ofU.S. Non-provisional Patent Application Ser. No. 13/051,507, filed onMar. 18, 2011, now U.S. Pat. No. 8,368,037, issued Feb. 5, 2013,entitled “Systems and Methods Providing Electron Beam Writing to aMedium,” which are hereby incorporated by reference in their entirety.

BACKGROUND

The present disclosure relates generally to semiconductor manufacturing.Specifically, the present disclosure relates to systems and methods thatwrite to a medium using electron beams.

Electron-beam (or “e-beam”) writing relates to a process for creatingchanges in a medium using e-beams. Specifically, some e-beam processesuse e-beams to write designs onto mediums. Examples of mediums that canbe written on with e-beams include semiconductor wafers and photomasks(e.g., fused silica and chrome masks). E-beam writing provides a way tocreate features on a medium where the features are smaller than aresolution limit for light.

Some conventional systems use a single-beam method to write designs to aphotomask. In one conventional system, in order to mitigate thebeam-stitching effect, multiple passes are made by a single beam toapply the desired dosages to the medium. Dosage refers to the amount ofelectron beam exposure at a given point or area, e.g., e-beam currentmultiplied by exposure time at a given area is a way to measure dosage.Assuming that the beam is kept at a constant current, dosage increaseswith a number of passes over an area. Furthermore, throughput istypically inversely proportional to dosage applied by a particular pass.Single-beam exposure methods may be undesirably slow for someapplications; thus some applications are evolving to a massive beamexposure technique.

Conventional massive beam exposure techniques employ a single sourcewith multiple apertures to generate parallel beams, where each of theparallel beams are individually controllable as to placement, size,dose, and blur. Also, the beams can be individually calibrated. In oneconventional technique, a set of parallel beams are used to writeparallel strips on a medium simultaneously. The beams are moved in thex-direction by deflection and in the y-direction by scanning movement ofthe medium to make a zigzag movement to apply a desired dosage andcreate the parallel strips.

However, one issue with conventional massive beam techniques isbeam-to-beam variation, and without some way to ameliorate beam-to-beamvariation, one or more of the strips may be different from other stripsand/or deviate from the desired dosage. Precise calibration for allbeams can be difficult, so some conventional techniques account forbeam-to-beam variation by overlapping the writing zones between adjacentbeams. The overlapped writing zones are referred to as stitches, andwhile not considered part of the strips, stitches are used to averagebeam-to-beam variation between adjacent beams.

The massive beam techniques can use Gaussian beams, where each beam is asingle beam, or patterned beams, where each beam includes a set ofsub-beams that are not individually controllable and are arranged in anarray.

The above-described conventional techniques have some disadvantages. Forinstance, as mentioned above, techniques using single beams withmultiple passes may be undesirably slow, i.e., throughput may not behigh enough for some applications. Also, some conventional massive beamtechniques using stitching may find throughput negatively affected bythe time used to write in the overlapped areas. More efficient andeffective e-beam writing is called for.

SUMMARY

The present disclosure provides for many different embodiments. In afirst embodiment, a method for electron-beam writing to a mediumincludes positioning the medium within an e-beam writing machine so thatthe medium is supported by a stage and is exposed to an e-beam source.The method also includes writing a pattern to the medium using aplurality of independently-controllable beams of the e-beam source, inwhich the pattern comprises a plurality of parallel strips. Each of theparallel strips is written using multiple ones of theindependently-controllable beams.

In another embodiment, an electron-beam writing system includes a stageupon which a medium may be placed and a writing mechanism to write uponthe medium placed upon the stage. The writing mechanism includes anelectron beam source operable to produce N independently-controllablebeams, where N is an integer larger than 1. The system also includes acomputer-based control system operable to write a pattern upon themedium in a plurality of parallel strips, each of the strips beingwritten using multiple ones of the N independently-controllable beams.

In another embodiment a method for electron-beam writing to a mediumincludes positioning an e-beam source to write a plurality of stripsonto the medium using N independently-controllable beams and writing toeach of the strips using multiple ones of the Nindependently-controllable beams. Variations among the respectiveindependently-controllable beams are averaged by writing to each stripusing a unique subset of the N independently-controllable beams.

BRIEF DESCRIPTION OF THE DRAWINGS

Aspects of the present disclosure are best understood from the followingdetailed description when read with the accompanying figures. It isemphasized that, in accordance with the standard practice in theindustry, various features are not drawn to scale. In fact, thedimensions of the various features may be arbitrarily increased orreduced for clarity of discussion.

FIG. 1 is a simplified diagram of an exemplary network system in whichembodiments may be implemented.

FIG. 2 is a simplified block diagram of an exemplary client computersystem that may be configured to implement embodiments.

FIG. 3 is an illustration of an exemplary process for performing e-beamwriting according to one embodiment.

FIG. 4 shows an exemplary medium with strips thereon according to oneembodiment.

FIG. 5 is an illustration of a portion of an exemplary medium accordingto one embodiment.

FIG. 6 is an illustration of an exemplary beam arrangement for use withan embodiment.

FIG. 7 is an illustration of the beam arrangement of FIG. 6 shown toemphasize the individual pixels of the sub-beams, where each dot in FIG.7 represents a sub-beam.

FIG. 8 shows an exemplary pixel projection along the x-directionaccording to one embodiment consistent with the examples above for FIGS.6 and 7.

FIG. 9 is an illustration of an exemplary x-direction projectionaccording to one embodiment that uses a beam-to-beam offset greater thanone pixel width.

FIG. 10 is an illustration of a 7×7 array of sub-beams for use with theembodiments of FIGS. 6-9.

DETAILED DESCRIPTION

The present disclosure relates generally to semiconductor manufacturing.Specifically, the present disclosure relates to e-beam writing systemsand methods that employ multiple beams. While the examples hereindiscuss applying the techniques to write to photolithographic masks andsemiconductor wafers, it is understood that the scope of embodiments caninclude any system for writing to any appropriate medium using e-beamtechnology.

The following disclosure provides many different embodiments, orexamples, for implementing different features of the invention. Specificexamples of components and arrangements are described below to simplifythe present disclosure. These are, of course, merely examples and arenot intended to be limiting. In addition, the present disclosure mayrepeat reference numerals and/or letters in the various examples. Thisrepetition is for the purpose of simplicity and clarity and does not initself dictate a relationship between the various embodiments and/orconfigurations discussed.

With reference now to the figures, FIG. 1 is a simplified diagram of anetwork system 100 in which embodiments may be implemented. Networksystem 100 includes a network 102 that provides a medium forcommunications between various devices and computers communicativelycoupled by network system 100. Network 102 may be implemented as one ormore of various networks, such as the Internet, an intranet, a localarea network, a wide area network (WAN), or another network architecturethat facilitates communications between network connected devices.Network 102 may include any one or more of various communicationconnections, such as wire, wireless, fiber optic, satellite links, orother communication media.

In the present example, various servers 110-112 are connected to network102. In addition, a client 120 is connected to network 102. Servers110-112 may be implemented as hypertext transfer protocol (HTTP)servers, file transfer protocol (FTP) servers, application servers, orother devices that provide data sources such as web pages or othercontent to client 120 connected therewith. Client 120 may be implementedas a personal computer, a portable computer, a network computer, a supercomputer, or another computational device.

Client 120 is connected to e-beam writing hardware 130, which receivesfiles from client 120 and writes to a physical medium according to thedata in the files. The data in the files includes layout patterns thatare stored and transmitted in a layout description language such asGDS-II or OASIS. E-beam writing hardware 130 in this example includeswriting mechanism 131, which includes a beam source and is operable toproduce multiple beams simultaneously, and stage 132, which supports themedium. Either or both of stage 132 and writing mechanism 131 may moveduring a writing process to facilitate patterning. For purposes of theexamples below, stage 132 is moved in the y-direction, and x-directionmotion is provided by deflection, though the scope of embodiments is notso limited, as other methods of writing motion are possible.

Computers, such as client 120 and/or servers 110-112 may provide controland data to e-beam writing hardware 130 to facilitate writing of designsto the medium. For instance, one or more computers may control themovement of stage 132 and/or deflection during writing processes.

FIG. 2 is a simplified block diagram of a computer system 200, such asclient 120 or any of servers 110-112 shown in FIG. 1, that may beconfigured to implement embodiments of an e-beam writing system.Computer system 200 includes a processor 202 interconnected with asystem bus 204. System bus 204 provides couplings to subsystems andcomponents of computer system 200. A memory controller 206interconnected with a system memory 208 provides a communicativecoupling between memory 208 and processor 202. Memory 208 may storeexecutable instructions that provide writing functionality as describedmore fully below. An input/output bridge 210 may be connected withsystem bus 204, and one or more input/output devices may be connectedwith an I/O bus 212. For example, a hard disk 216 (or other memory, suchas a flash drive) may provide non-transitory, non-volatile storage, anda modem or network adapter 214 may provide a communication interfacethat facilitates communication exchanges between computer system 200 andone or more data resources on a network. Additionally, user inputdevices, such as a mouse/keyboard 218, may be coupled with I/O bus 212and facilitate user input to computer system 200. The configuration ofcomputer system 200 is illustrative and is chosen only to facilitate anunderstanding of embodiments described herein.

FIG. 3 is an illustration of exemplary process 300 for performing e-beamwriting according to one embodiment. Process 300 may be performed, forexample, by one or more computers 110-112, 120 and e-beam writinghardware 130 of FIG. 1. In block 305, the medium is positioned withinthe e-beam writing machine so that it is supported by the stage andexposed to the e-beam writing source.

The system writes a pattern to the medium, where the pattern is made ofmultiple parallel strips. Block 305 may further include calibrating thee-beam source so that it can produce N independently-controllable beams,where N is an integer larger than one. Furthermore, block 305 may alsoinclude setting a placement, size, and dose for each of the beams.

In block 315, writing is performed on the medium using the Nindependently-controllable beams. In this example, each of the parallelstrips is written using more than one of the beams, though perhaps fewerthan all N beams.

Further in this example, each of the strips is an area of the mediumwith a single e-beam dosage, the effects of beam-to-beam variationnotwithstanding. Example strips are shown in FIGS. 4 and 5. It isunderstood that beam-to-beam variation may cause dosage to vary somewhatwithin the bounds of a single strip; however, the use of multiple beamsto write to a given strip mitigates the variation within a single stripand among multiple strips.

The e-beam writing process includes writing to a physical medium. In oneexample, the e-beam writing process is used to etch material from asemiconductor wafer in a design that facilitates the manufacture ofstructures on the wafer. In an other example, the e-beam writing processis used to remove portions of a photomask that is made of e.g., chromeand fused silica. The photomask can then be used in the manufacturingprocess of semiconductor devices. E-beam writing processes provide aneffective way to create designs on a physical medium where some of thefeatures of the design may be too small to be made by other conventionalprocesses, such as photolithography.

The scope of embodiments is not limited to the example shown in FIG. 3.Other embodiments may add, omit, rearrange, or modify actions. Forinstance, some embodiments may repeat the actions of FIG. 3 many timesto write multiple complex structures to the medium. Furthermore, otherembodiments include subsequent processing steps appropriate for aphotomask, semiconductor wafer, or other medium.

As shown below, some example embodiments include use of deflection towrite a zigzag path using each of the beams. In other embodiments,either scanning or deflection is used to provide relative motion forwriting. Still further, some embodiments employ Gaussian beams, whereasother embodiments employ patterned beams.

Moving to FIG. 4, a medium 400 with strips 401 thereon is depictedaccording to one embodiment during e-beam writing. Dot 402 represents aplacement at a point in time of one e-beam, and other dots in FIG. 4represent other e-beams similarly.

In FIG. 4, the area of each strip 401 is double exposed. Lines 410 showan example path traced by the e-beam of strip 401 a. In FIG. 4, thestage (not shown) moves in the y-direction, and deflection is used tocreate relative movement in the x-direction. The result is the pathrepresented by lines 410.

The dot adjacent dot 402 represents a beam that also writes to strip 401a in a manner similar to that described immediately above. The two beamstogether write strip 401 a. Portions 404 and 405 are shown as not doubleexposed, though various embodiments include techniques to ensure thatportions 404, 405 are double exposed. For instance, dummy exposures maybe used to double expose portions 404, 405. Also, the stage can be usedto position the medium to make further exposures where desired toprovide consistent double exposure throughout medium 400. In someembodiments, the technique illustrated in FIG. 4 brings superiorbeam-to-beam uniformity than conventional stitching techniques discussedabove. Of note in the embodiment of FIG. 4 is that each strip 401 iscreated using a unique set of beams.

In some embodiments, throughput is not adversely affected by tying updouble the beams on a single set of strips. If the desired dose for astrip 401 is one unit, the beams can be kept at one current unit whiledoubling writing speed to two speed units. Since each strip 401 isdouble exposed, the cumulative dose for each strip is one unit, and itis performed in one-half time unit because the writing velocity isdoubled. The beams can then be moved to a different but similarly-sizedportion of the medium to write a unit dose in another one-half timeunit. Thus, the beams can be fully utilized in a given time unit. A ruleof thumb for some embodiments is that velocity is increased by a factorequal to the exposure factor so as to achieve the same throughput.

FIG. 5 is an illustration of portion 500 of a medium according to oneembodiment during e-beam writing. In the example of FIG. 5, strips 501are quadruple exposed by the end of the process, and line 510 shows anexample path written by a beam that is represented by dot 502. Strips501 a, 501 c, and 501 d are shown as having less than quadrupleexposure. Only strip 501 b falls within quadruple exposure area 501,whereas strips 501 a, 501 c, and 501 d fall within exposure areas 504,505 with less than quadruple exposure. As explained above with respectto FIG. 4, various techniques may be used to provide consistentquadruple exposure. For instance, in one example, dummy exposures may beadded to strips 501 a, 501 c, and 501 d.

Additionally and/or alternatively, the beams can be moved to the rightor to the left adjacent the end beam on that side, where writing isbegun. For instance, in the present example, there are ten beamsrepresented by ten dots 502. After the beams have traversed the medium,the stage can be moved to position the medium so that the ten beams aremoved in the x-direction ten places and begin writing to the immediateright (or left) of the original ten beams, thereby writing additionalstrips and providing quadruple exposure to areas 504 (and/or 505). Suchoperation can be performed in any embodiment using any number of beamsper strip.

Once again, the operation illustrated by FIG. 5 may be performed to haveno negative impact on throughput. For instance, similarly to theoperation described above for FIG. 4, the writing speed can be increasedby the exposure factor. In fact, in the embodiments of FIGS. 4 and 5,the writing speed can be changed by any arbitrary factor to increase ordecrease throughput as appropriate.

FIG. 6 is an illustration of exemplary beam arrangement 600 for use withan embodiment. Beam arrangement 600 includes fourindependently-controllable beams 610, 620, 630, 640. Each of theindependently-controllable beams 610, 620, 630, 640 includes an M×Marray of sub-beams, where M is an integer greater than one (and in thiscase is equal to seven). In other embodiments, M can be any arbitraryinteger greater than one.

The sub-beams are illustrated in FIG. 6 by exemplary sub-beams 611 (inbeam 610), 621 (in beam 620), 631 (in beam 630), and 641 (in beam 640).The sub-beams themselves are not independently-controllable.

Beam 640 is overlaid by beam 630, which is overlaid by beam 620, whichis overlaid by beam 610. Between each adjacent beam there is an x-yoffset so that the beams 610, 620, 630, 640 do not lay directly on topof each other. Furthermore, there is an angular offset, alpha, withrespect to a direction of scanning (in this case, it assumed that thedirection of scanning is along the y-direction). Furthermore, in thisembodiment, x-direction movement is not used when scanning a givenstrip, so that the movement relevant to the discussion of FIGS. 6 and 7is the y-direction movement.

FIG. 7 is an illustration of beam arrangement 600 shown to emphasize theindividual pixels covered by the sub-beams, where each dot in FIG. 7represents a sub-beam. The dots in FIG. 7 are an aggregation of the four7×7 arrays of sub-beams shown in FIG. 6, for a total of 196 sub-beams.FIG. 7 also illustrates an exemplary scan direction and an angularoffset. During writing, the beams are projected onto the medium as shownin FIGS. 6 and 7, and the medium is moved relative to the beam sourcesto provide scanning movement. The beams 610, 620, 630, 640, areperformed simultaneously in this example.

View 710 is an illustration of the projection of the pixels along a lineperpendicular to the scan direction. The x-y offset and angular offsetproduce a configuration wherein adjacent pixels are from differentbeams. In the case of view 710, the first pixel is from beam 610, thesecond pixel is from beam 620, the third pixel is from beam 630, and thefourth pixel is from beam 640. The placement then repeats across theview in the x-direction. View 710 illustrates that a strip written bybeam arrangement 600 includes contributions from four different beams610, 620, 630, 640, and the sub-beams of those beams are distributed ina way that averages out the beam-to-beam variation among beams 610, 620,630, 640.

FIG. 8 is an exemplary pixel projection along the x-direction accordingto one embodiment consistent with the examples above for FIGS. 6 and 7.In the embodiments of FIGS. 6-8, each strip is covered by multipleindependent beams, and adjacent pixels are exposed by different beams.In FIG. 8, strip 1 is exposed by a set of four independent beams, andstrip 2 is exposed by a different set of four independent beams. Whilenot shown in FIG. 8, it is noted that different sets of beams can beused to expose either or both of strips 1 and 2 in subsequent exposures.The subsequent exposures can further reduce the effects of beam-to-beamvariation and also enable gray-level writing.

In FIG. 8, the x-y and angular offsets combine to make a cumulativeoffset substantially equal to one pixel width. The one-pixel-widthoffset creates the pattern shown in FIGS. 7 and 8, where the pixels havea repeating pattern along the x-direction (perpendicular to they-direction scanning).

Other embodiments may use a cumulative beam-to-beam offset that isgreater than one pixel width. FIG. 9 is an illustration of an exemplaryx-direction projection according to one embodiment that uses abeam-to-beam offset greater than one pixel width. The combination ofbeams to cover a given strip is not fixed or regular in the example ofFIG. 9. Each strip is exposed by different combinations of individualbeams, which further mitigates the effects of beam-to-beam variation.Strips 1 and 3 are shown as being not exposed with the same dose asstrip 2, but it is understood that the number of strips extends beyondstrip 1 and strip 3, and beams writing those additional strips (notshown) add pixels to strips 1 and 3 to apply a consistent exposure.

The examples above in FIGS. 6-9 show example embodiments using four oreight beams, though the scope of embodiments is not so limited. Rather,various embodiments may include any arbitrary number of beams.Furthermore, x- and y-directions are used purely for illustration and donot limit the various embodiments to any particular orientation.

FIG. 10 is an illustration of a 7×7 array 1000 of sub-beams for use withthe embodiments of FIGS. 6-9. Pb is a spacing between sub-beams in array1000. Pproj is a width of a sub-beam as it is projected onto the medium.Alpha is the angular offset. In this example, a pixel size is 3.5 nm.The equations below show the area covered per scan in this example. Itis noted that the e-beam current and the writing speed can be adjustedin view of the below equations to have a desired effect on throughput.The numbers below are for illustration only and do not limit the scopeof embodiments.

consider  P_(proj)  is  the  multiple  of  3.5  nm  pixel  sizeP_(proj) = P_(b) ⋅ sin (α_(array)) = 10.5  nm = 3 × 3.5  nm ⇒ P_(b) = 74.25  nmBeam  Shift = 1  pixel If  w_(proj) = Strip  Width${N_{subbeams}\mspace{14mu}{along}\mspace{14mu} w_{proj}} = {\frac{w_{proj}}{PixSize} = {\frac{504\mspace{14mu}{nm}}{3.5\mspace{14mu}{nm}} = 144}}$${N_{beams}\mspace{14mu}{for}\mspace{14mu} 1\mspace{14mu}{Strip}} = {\frac{N_{subbeams}\mspace{14mu}{along}\mspace{14mu} w_{proj}}{N_{{subbeams}\mspace{14mu}{array}}} = {\frac{144}{7} = 21}}$${N_{strip}\mspace{14mu}{per}\mspace{14mu}{Scan}} = {\frac{{Total}\mspace{14mu}{Beam}\mspace{14mu}{Number}}{N_{beams}\mspace{14mu}{for}\mspace{14mu} 1\mspace{14mu}{Strip}} = {\frac{13000}{21} = 619}}$Area  Covered  per  Scan = N_(strip)  per  Scan × w_(proj) = 619 × 504  nm = 0.312  mm

Various embodiments may include advantages over other techniques. Forinstance, various embodiment write to each strip using multiple beams,thereby helping to average out beam-to-beam variation without stitching.It is understood that the embodiments illustrated above may not in allscenarios completely eliminate beam-to-beam variation. However, it isenough for many applications that the beam-to-beam variation ismitigated by use of multiple beams per strip. Furthermore, as explainedabove, parameters (e.g., e-beam current and writing speed) can beadjusted so that the effect on throughput is not negative in someinstances. Additionally, some embodiments perform gray-level writing byapplying the multi-pass writing technique described above.

The foregoing has outlined features of several embodiments so that thoseskilled in the art may better understand the detailed description thatfollows. Those skilled in the art should appreciate that they mayreadily use the present disclosure as a basis for designing or modifyingother processes and structures for carrying out the same purposes and/orachieving the same advantages of the embodiments introduced herein.Those skilled in the art should also realize that such equivalentconstructions do not depart from the spirit and scope of the presentdisclosure, and that they may make various changes, substitutions andalterations herein without departing from the spirit and scope of thepresent disclosure.

What is claimed is:
 1. A method for electron-beam writing to a medium comprising: producing a plurality of independently-controllable beams, in which the independently-controllable beams each comprise a patterned beam with an array of M×M non-independent sub-beams, the independently-controllable beams being overlaid with an offset relative to each other; and writing a pattern to the medium using the plurality of independently-controllable beams, wherein the pattern comprises a plurality of strips, and further wherein at least one of the strips is written using multiple ones of the independently-controllable beams to cause multiple beam exposures to areas of at least one of the strips.
 2. The method of claim 1 in which the strips are not separated by stitches.
 3. The method of claim 1 in which each of the independently-controllable beams comprises a Gaussian beam.
 4. The method of claim 1 in which each of the independently-controllable beams are applied in a zigzag configuration.
 5. The method of claim 4 in which each of the independently-controllable beams has a zigzag pattern that overlaps with at least one adjacent beam.
 6. The method of claim 1 in which a writing velocity of the independently-controllable beams is increased by a factor of N, where N is an integer equal to a number of the independently-controllable beams that write to a single one of the strips.
 7. A method for electron-beam writing to a medium comprising: producing a plurality of independently-controllable beams with an electron beam source, in which the independently-controllable beams each comprise a patterned beam with an array of M×M non-independent sub-beams, the independently-controllable beams being overlaid with an offset relative to each other; and writing a pattern to the medium using the plurality of independently-controllable beams, in which the pattern comprises a plurality of areas, and further in which at least one of the areas is written using multiple ones of the independently-controllable beams to cause multiple beam exposure to at least one of the plurality of areas.
 8. The method of claim 7 in which the medium comprises one of: a semiconductor wafer and a photomask.
 9. The method of claim 7 in which each of the areas comprises a single, respective electron beam dosage.
 10. The method of claim 7 in which the independently-controllable beams are applied using at least one of: electron beam deflection and relative movement of the medium to the electron beam source.
 11. An electron-beam writing system, the system comprising: a medium support stage; a writing mechanism, the writing mechanism comprising an electron beam source operable to produce N independently-controllable beams, where N is an integer larger than 1, in which the independently-controllable beams each comprise a patterned beam with an array of M×M non-independent sub-beams, the independently-controllable beams being overlaid with an offset relative to each other and an angular offset relative to a direction of scanning so that a projection of the independently-controllable beams on the medium has a pattern in which adjacent pixels are from different ones of the independently-controllable beams; and a computer-based control system operable to: produce multiple ones of the N independently-controllable beams to cause multiple beam exposure to a predefined area over the medium support stage.
 12. The system of claim 11 in which the independently-controllable beams comprise Gaussian beams, and in which the computer-based control system writes with the Gaussian beams using movement in x- and y-directions.
 13. The system of claim 11 in which each of the independently-controllable beams are applied in a zigzag configuration.
 14. The system of claim 11 in which each of the independently-controllable beams has a zigzag pattern that overlaps with at least one adjacent beam.
 15. The system of claim 11, wherein the medium comprises one of: a semiconductor wafer and a photomask.
 16. The system of claim 11 in which the independently-controllable beams are applied using at least one of: electron beam deflection and relative movement of the medium to the electron beam source.
 17. The method of claim 16 in which each of the independently-controllable beams comprises a Gaussian beam.
 18. The method of claim 17 in which each of the independently-controllable beams is written in a zigzag path in each strip using at least one of deflection and relative movement of the medium and the electron beam source.
 19. The method of claim 16 in which a motion of the independently-controllable beams uses straight-line scanning and wherein, for each of the plurality of strips, the independently-controllable beams are applied simultaneously.
 20. The method of claim 1, in which the independently-controllable beams are overlaid with an angular offset relative to a direction of scanning such that a projection of the independently-controllable beams on the medium has a pattern in which adjacent pixels are from different ones of the independently-controllable beams. 